Injective function that is not surjective

Question

I'm trying to find an example of a continuously differentiable function from $\mathbb{R}$ to $\mathbb{R}$ that is injective but not surjective.

I can easily find one from $\mathbb{Z}$ to $\mathbb{Z}$ but I'm having difficulty finding one for the reals.

What's the one you have for the Integers? – JB King Mar 05 '13 at 00:11 — JB King, Mar 05 '13 at 00:11

Alex Youcis · Answer 1 · 2013-03-05T00:07:16.260

34

Hint: It might be easier than expected.

edited Mar 05 '13 at 00:07

answered Mar 04 '13 at 20:58

Alex Youcis

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+2 for cleverness in delivery! Okay, I guess I can't do that. Well, +1, anyway. – Cameron Buie Mar 04 '13 at 21:02
That's a good one, +1. – Julien Mar 04 '13 at 21:02
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He wanted a function, not a punction ;) – Hagen von Eitzen Mar 04 '13 at 21:24
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@HagenvonEitzen This thread's only big enough for one pun master--so you can just git out. – Alex Youcis Mar 04 '13 at 21:31
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Punny, we are all so punny here. – JB King Mar 04 '13 at 23:15
It's kind of interesting that ** ** came out as italics + asterisks and not bold. – Alexander Gruber Mar 04 '13 at 23:19
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@AlexanderGruber: Yeah, it's strange. My guess is that the **...** notation for bold was invalidated because the closing ** was followed immediately by letters, whereas the inner *...* notation for italics did not have that issue. To work around this in a question or an answer (but not in a comment), one can use the HTML-style notation: easier than <b>exp</b>ected. – ruakh Mar 04 '13 at 23:41
@ruakh Thanks for the tip :) – Alex Youcis Mar 05 '13 at 00:07

1 Answers1